Detail X: A Case Study IV

Under normal circumstances, I would place the rivers at this point. However, I am adding them by hand. Rivers are saved as a list of the hexes through which they flow, which makes this part more or less trivial. The Strahler numbers are saved for each in-flow hex and so the width of the river can be drawn accurately.

Hex 25; river in white temporarily for emphasis

The next step is determining which hexes are settled and which are wild. The infrastructure for Hex 25 is $I=16$. This isn't quite as simple as placing, for instance, 16 of 400 hexes as "settled." I reviewed the system for determining the relationship between infrastructure and number of settled hexes back in Detail III: Infrastructure. Briefly, each hex contributes to the total infrastructure based on the number of settled hexes that it itself borders.

There are then two broad scenarios for placing these hexes. The first is the case here, where I already know the "core" location of the main settlement within the hex. I want the other settled hexes to "cluster" around this one, so the base chance of settlement ($P_s = I/400$) is modified based on proximity to the constraints (there may be more than one in other cases): \[P_s = \left(\frac{I}{400}\right)^{|s - c|\cdot t}\], where $|s-c|$ is the distance between the 1-mile hex $s$ and the constraint $c$, and $t$ is a factor such that the sum of probabilities is equal to $I$. This added factor makes convergence a lot faster. Thanks to Scott for this idea!

For now I'm coding the settled hexes as grassland. The algorithm yields two Type VII hexes (1) and four Type VI hexes (2) for a total of $2\times1 + 4\times2 = 16 = I$. Perfect! In this case, they are all contiguous, but this need not be the case. Just luck of the draw and a consequence of the low overall infrastructure. 16 is really not very much at all.

The second scenario (and honestly, more common) is a 20-hex without a named settlement, and thus no specific constraint. Settled hexes will then tend to cluster around river features or roads. Therefore, we can do a similar adjustment with the distance to a random river or road:

However, most of the 20-hexes I'm looking at initially will have settlement features. This will come in handy later on.